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In this paper we obtain an existence result for an wide class of problems involving variable exponents which are related to several applications in electrorheological fluids and image processing. Under additional conditions it is obtained the multiplicity of solutions. It is also presented examples of applicability of the results. The arguments are based on sub-supersolutions and appropriatedestimates in the variable spaces setting.

Multiple solutions for a class of problems involving the p(x) -Laplacian operator